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JBMO TST - Macedonia
2016 Macedonia JBMO TST
5
5
Part of
2016 Macedonia JBMO TST
Problems
(1)
2016 JBMO TST- Macedonia, problem 5
Source: 2016 JBMO TST- Macedonia
5/27/2019
Solve the following equation in the set of positive integers
x
+
y
2
+
(
G
C
D
(
x
,
y
)
)
2
=
x
y
ā
G
C
D
(
x
,
y
)
x + y^2 + (GCD(x, y))^2 = xy \cdot GCD(x, y)
x
+
y
2
+
(
GC
D
(
x
,
y
)
)
2
=
x
y
ā
GC
D
(
x
,
y
)
.
Junior
JMMO
2016
number theory
Macedonia
greatest common divisor